Sedimentation of solid particles is a basic phenomenon which impacts a wide range of applications and naturally-occurring phenomena. In fact, gravitationally-driven sedimentation and centrifugation are among the simplest and most widely-practiced techniques for liquid-solid separation, used for processes from industrial-scale water clarification to medical laboratory separation of blood components. As a consequence, sedimentation has a long history of study.
Settling in non-Newtonian fluids is of interest in a number of industrial contexts. Often, the goal is to minimize the sedimentation rate. For example, foodstuffs such as jams and yogurt are preferred to have uniform mixing of the solid fruit and seeds with the suspending continuous material. In cement and concrete, settling-induced separation of sand and aggregate particles from the cement paste is highly undesirable, and specialized transportation equipment, e.g., a rotating mixer truck, have been designed to maintain uniform mixing. In general, the methods available for minimizing settling are constrained by processing or end-product demands on the mixture (e.g., texture of a food product, flowability of concrete, etc.).
In hydraulic fracturing, large liquid pressure provided by pumps at the surface of the earth is used to pump a type of servicing fluid, referred to as a carrying fluid, through a wellbore into a subterranean zone at a rate and pressure such that fractures are formed or enhanced in a petroleum-bearing formation. It is to be understood that “subterranean formation” encompasses both areas below exposed earth and areas below earth covered by water such as ocean or fresh water. This is typically followed by the pumping of a carrying fluid having a slurry of solid particles (e.g., sand, an engineered material such as sintered bauxite or alumina, etc.) dispersed therein into the resulting fracture to hold or “prop” the fracture open when the fracturing pressure is removed and production of petroleum commences. The “proppant” particles then become deposited in the fracture and these particles function, inter alia, to hold the fracture open while maintaining conductive channels through which produced fluids may flow upon completion of the fracturing treatment and to release of the attendant hydraulic pressure.
The balance between flow properties and settling characteristics is central to hydraulic fracturing for petroleum well stimulation. For example, quality performance demands that the proppant be placed deep within the fracture, which requires that the excess weight of the solid proppant be supported during flow of the carrying fluid. It is desirable for the solid particles to be uniformly distributed for maximum effectiveness as a proppant and to minimize settling, which may be excessively rapid and detrimental to the process. In principle, settling rates can be reduced by increasing the viscosity of the slurry or carrying liquid, but this option is limited by the large distances under the surface at which the treatments are typically placed and the consequent large pressure drops associated with pumping. As a consequence, the liquids used for proppant slurries are typically viscoelastic polymeric solutions, gels, emulsions, or foams, with aqueous solutions of the naturally-occurring long-chain polymer guar being among the most common. To support the weight of proppants sufficiently well in many applications, it has been found that cross-linking (reversibly or irreversibly) of the guar solution results in an effective suspending medium without excessive viscosity to limit the pumpability of the liquid or slurries formed from it.
Rheology includes the study of the deformation and flow of matter. The rheology of reversible borate cross-linking of guar has been extensively studied. It has been found that shear history has less influence in reversibly cross-linked systems such as borate cross-linked guar than in permanently cross-linked systems, such as a zirconium cross-linked guar. In small-amplitude oscillatory measurements, reversibly cross-linked materials obey linear viscoelastic models, such as a Maxwell model. At high steady shear rates, reversibly cross-linked samples behave similarly to permanently cross-linked gels, which often break into domains and slip. Despite this knowledge, particle motion in reversibly cross-linked solutions under static settling and dynamic conditions is far from fully understood.
It is desirable to test particle-laden fluids or systems to determine if they are suitable for their intended use. However, in particle-laden fluids or suspensions, the particulate matter has a tendency to settle during an experiment, thereby often resulting in inaccurate measurements. Conventional rheometers do not take into account this settling effect in particle-laden fluids, nor do they maintain particle-laden fluids in suspension. Accordingly, reliable testing of the effect of particle settling on particle-laden fluids has been problematic due to the fact that existing rheometers have been unable to measure to a desired accuracy the rheological properties (e.g., viscosity) of a fluid having a high concentration of solids or particles.
Thus, it would be desirable to create methods of estimating proppant transport and the ability of non-Newtonian fluids to suspend particles, in order to assist in correlating base fluid rheology with particle settling, thereby allowing estimation of slurry transport efficiency and design of new fracturing fluid systems.
While the invention is susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and will be described in detail herein. It should be understood, however, that the invention is not intended to be limited to the particular forms disclosed. Rather, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.